to me there is a specific moment where he starts to believe that katniss could have some real affection for him. i feel that before this point he's going along with her strategy but definitely wondering exactly what's happening. the first time katniss's kisses him he's high on fever so who knows what's going on inside his mind. afterwards he's definitely trying to figure her out - are they playing it up for the cameras? for the attention? is there some honesty here?
now the fact that he forbids katniss to go for his medicine already tells me that he assumes she's been acting and/or being nice because he's dying. at that point he has written himself off. but then she actually goes to the cornucopia, risks her life and peeta's mad. and this is that turning point:
“the problem is we’re both still alive. which only reinforces the idea in your mind that you did the right thing,” says peeta.
“i did do the right thing,” i say.
“no! just don’t, katniss!” his grip tightens, hurting my hand, and there’s real anger in his voice. “don’t die for me. you won’t be doing me any favors. all right?”
i’m startled by his intensity but recognize an excellent opportunity for getting food, so i try to keep up. “maybe i did it for myself, peeta, did you ever think of that? maybe you aren’t the only one who... who worries about... what it would be like if...”
i fumble. i’m not as smooth with words as peeta. and while i was talking, the idea of actually losing peeta hit me again and i realized how much i don’t want him to die. and it’s not about the sponsors. and it’s not about what will happen back home. and it’s not just that i don’t want to be alone. it’s him. i do not want to lose the boy with the bread.
“if what, katniss?” he says softly.
i wish i could pull the shutters closed, blocking out this moment from the prying eyes of panem. even if it means losing food. whatever i’m feeling, it’s no one’s business but mine. “that’s exactly the kind of topic haymitch told me to steer clear of,” i say evasively, although haymitch never said anything of the kind. in fact, he’s probably cursing me out right now for dropping the ball during such an emotionally charged moment. but peeta somehow catches it.
“then i’ll just have to fill in the blanks myself,” he says, and moves in to me.
from this point on he thinks that whatever is happening between them is real (and it is). i do think he's aware that capitol is watching but he's perceptive and he believes her (and she's not lying, this is the kiss that makes her want another). and then she ends up wanting to die for him, and even before the berries he's trying to get her to kill him, so he doesn't think she is crazy about him or something. he isn't upset at all when she points her arrow at him out of fear. but then she wants to die for him. and he still knows that they're trying to outsmart the gamemakers (hold them out for everyone to see and the fact that he does not swallow them) but he's also honest (and so is she). for the first time in his life (headcanon but really supported by text) somebody is choosing him. and then they win and katniss hides in his shirt and runs into his arms and he thinks that he got something good out of this. but then they're on that train and somehow haymitch gets involved and now instead of this being a game between him and katniss on their terms there's someone else and his teenage angst and childhood trauma get the best of him and he closes himself off and katniss obviously, due to her own teenage angst and childhood trauma, can't figure out what she's feeling. it's just a mess. that's the whole point. a set up for their entire relationship during the trilogy. real or not real.
(i did write a little more on exactly what i think peeta's feeling during this scene in the tags here)